Draft version August 7, 2018Typeset using LATEX twocolumn style in AASTeX61

X-RAY LUMINOSITY AND SIZE RELATIONSHIP OF SUPERNOVA REMNANTS IN THE LMC

Po-Sheng Ou (歐柏昇),1, 2 You-Hua Chu (朱有花),1, 2, 3 Pierre Maggi,4 Chuan-Jui Li (李傳睿),1, 2

Un Pang Chang (曾遠鵬),2 and Robert A. Gruendl3, 5

1Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141, Taipei 10617, Taiwan, R.O.C.

psou@asiaa.sinica.edu.tw2Department of Physics, National Taiwan University, Taipei 10617, Taiwan, R.O.C.3Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 West Green Street,

Urbana,IL 61801, U.S.A.4Departement d’Astrophysique, IRFU, CEA, Universite Paris-Saclay, F-91191 Gif-sur-Yvette, France.5National Center for Supercomputing Applications, 1205 West Clark St., Urbana, IL 61801, U.S.A.

ABSTRACT

The Large Magellanic Cloud (LMC) has ∼60 confirmed supernova remnants (SNRs). Because of the known distance,

50 kpc, the SNRs’ angular sizes can be converted to linear sizes, and their X-ray observations can be used to assess

X-ray luminosities (LX). We have critically examined the LMC SNRs’ sizes reported in the literature to determine

the most plausible sizes. These sizes and the LX determined from XMM-Newton observations are used to investigate

their relationship in order to explore the environmental and evolutionary effects on the X-ray properties of SNRs. We

find: (1) Small LMC SNRs, a few to 10 pc in size, are all of Type Ia with LX > 1036 ergs s−1. The scarcity of small

core-collapse (CC) SNRs is a result of CCSNe exploding in the low-density interiors of interstellar bubbles blown by

their massive progenitors during their main sequence phase. (2) Medium-sized (10-30 pc) CC SNRs show bifurcation

in LX , with the X-ray-bright SNRs either in an environment associated with molecular clouds or containing pulsars

and pulsar wind nebulae and the X-ray-faint SNRs being located in low-density interstellar environments. (3) Large

(size>30 pc) SNRs show a trend of LX fading with size, although the scatter is large. The observed relationship

between LX and sizes can help constrain models of SNR evolution.

Keywords: ISM: supernova remnants — supernovae: general — X-rays: ISM — Magellanic Clouds

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1. INTRODUCTION

Most supernova remnants (SNRs), regardless of pro-

genitor types, exhibit some kind of X-ray emission.

Thermal emission can arise from shocked interstellar

medium (ISM) and/or SN ejecta, while relativisic elec-

trons interacting with amplified magnetic field can pro-

duce non-thermal (synchrotron) emission. In the cases

of core-collapse (CC) SNRs, there may exist additional

X-ray emission from pulsars and pulsar wind nebulae

(PWNe). See Vink (2012) for a comprehensive review

of X-ray emission from SNRs.

To make a statistical study of X-ray emission of SNRs,

we need a large sample of SNRs with known distances.

The Galactic sample of SNRs is quite incomplete be-

cause of heavy absorption in the Galactic plane, and

the distances to individual SNRs are often very uncer-

tain. The Large Magellanic Cloud (LMC), on the other

hand, has small internal and foreground absorption col-

umn densities (Schlegel et al. 1998), and hosts a large

sample of SNRs all at essentially the same known dis-

tance 50 kpc1 (Pietrzynski et al. 2013). At least 59 SNRs

have been confirmed and a few additional SNR candi-

dates have been suggested (Maggi et al. 2016; Bozzetto

et al. 2017). This large sample of LMC SNRs is ideal

for systematic and statistical studies of X-ray emission

from SNRs.

Recently, Maggi et al. (2016) analyzed XMM-Newton

observations of the 59 confirmed SNRs in the LMC, de-

riving physical properties of the X-ray-emitting plasma

from spectral fits. Because of the known distance, it

is possible to determine the X-ray luminosity of each

SNR. In the meantime, Bozzetto et al. (2017, hereafter

Bo2017) measured the sizes of the 59 LMC SNRs using

X-ray, radio and optical images. Intrigued by these re-

sults, we have examined the relationship between X-ray

luminosity and size of LMC SNRs in order to explore

evolutionary effects and environmental impacts on X-

ray properties of SNRs.

This paper reports our investigation of the relation-

ship between X-ray luminosity and size of SNRs in the

LMC. In Section 2, we discuss the physical meaning of

SNR sizes measured at optical or X-ray wavelengths,

examine the SNR sizes reported in the literature, and

assess the most reliable sizes that represent the SNRs’

full extent. In Section 3, we plot X-ray luminosities

against sizes for LMC SNRs and note intriguing fea-

1 Note that due to the LMC’s inclination of 18-23 degrees inthe line of sight, the error in the distance and linear size can beuncertain by up to 10% (Subramanian & Subramaniam 2010),and the luminosity can be uncertain by 20%. These uncertainties,however, do not affect the general conclusions of these paper.

tures in the distribution of SNRs in this plot. In Section

4, we discuss the physical reasons behind the distribu-

tion of SNRs in the plot of X-ray luminosity versus size.

Finally, a summary is given in Section 5.

2. SIZES OF LMC SNRS

Both X-ray and optical images have been used to mea-

sure SNR sizes, but it should be noted that while X-

ray and optical Hα emission both originate from post-

shock gas, they arise under different physical conditions.

Generally speaking, X-ray emission comes from hot gas

with temperatures & 106K, while Hα emission originates

from ionized gas at ∼ 104K; therefore, an SNR size mea-

sured in X-rays may differ from that measured in Hα.

Measurements of X-ray and Hα sizes of SNRs can

also differ because of different instrumental sensitivi-

ties. For example, the XMM-Newton observations of the

LMC SNRs detect volume emission measures (EMV ≡∫nenHdV , where ne is the electron density, nH is the

hydrogen density, and V is the emitting volume) of 1054

– 1060 cm−3 (Maggi et al. 2016). For a spherical vol-

ume of highly ionized interstellar gas (ne/nH ∼ 1.2 for

a typical helium to hydrogen number ratio of 0.1), the

rms density derived from the volume emission measure

is

〈n2H〉1/2 =

(5 EMV

πfD3

)1/2

, (1)

where D is the diameter of the X-ray emitting gas, and f

is the volume filling factor. For SN ejecta dominated by

heavy elements, ne/nH should be greater than 1.2, and

hence the rms hydrogen density in equation (1) is the

upper limit, which is about (0.001–3) f−1/2 cm−3 for

the LMC SNRs as derived from the XMM-Newton mea-

surements. Meanwhile, narrow-band Hα CCD images

can easily detect emission measures (EM` ≡∫nenHd`,

where ` is the emitting path length) down to 10–20 cm−6

pc, and for an emitting path length of 5 pc the electron

density needs to be at least 1.4–2 cm−3. Thus, for SNRs

running into a dense medium with densities > 1 H-atom

cm−3, the shocked gas can be detected in both X-ray and

optical wavelengths, while those running into a medium

with densities�1 H-atom cm−3 may be visible in X-rays

but not in optical.

Another factor that can affect the measurements of

SNR sizes is the wavelength-dependent confusion from

the background. SNRs may be located adjacent to

HII regions or superposed on a complex background, in

which case the boundary of an SNR can be diagnosed by

sharp filamentary morphology, enhanced [S II] line emis-

sion, high-velocity components in optical emission lines,

nonthermal radio emission, and diffuse X-ray emission

(Chu 1997). When more than one of the above diag-

3

Figure 1. The left panels compare the SNR sizes reported by De2010 and Bo2017, with the upper panel plotting De2010 sizesversus Bo2017 sizes and the lower panel plotting the (De2010 size / Bo2017 size) ratios versus Bo2017 sizes. The right panelscompare the SNR sizes reported by Ba2010 and Bo2017 in the same way as the left panels.

nostics are detected, the SNR boundary can be more

reliably measured. However, if X-ray emission is the

only diagnostic detected and the SNR emission is super-

posed on a large-scale diffuse X-ray emission, the back-

ground confusion can prevent accurate measurements of

the SNR size.

Several publications have reported sizes of the LMC

SNRs, but there are often discrepancies between their

measurements. Badenes et al. (2010, hereafter Ba2010)

used mainly X-ray images from Chandra or XMM-

Newton to determine the SNR sizes, and adopted

previous optical and radio measurements when high-

resolution X-ray images were not available. Desai et al.

(2010, hereafter De2010) considered optical and X-ray

images, and measured SNR sizes based on the extent

of diffuse X-ray emission or filamentary Hα shell struc-

ture. Bo2017 considered optical, X-ray and radio im-

ages. Maggi et al. (2016) also listed SNR sizes, but they

only gave the maximal diameters in X-ray; thus these

sizes are often much larger than the ones reported by

the above three references. Below we compare the SNR

sizes reported by Ba2010, De2010, and Bo2017.

Bo2017 has the largest and most complete SNR sam-

ple, and is thus chosen to be the reference for compar-

isons. Figure 1 compares SNR sizes reported by De2010

and Bo2017 in the left panels, and Ba2010 and Bo2017

in the right panels. The upper panels plot SNR sizes

from one source versus another, while the lower panels

plot the ratios of SNR sizes from two sources.

De2010 and Bo2017 both used primarily optical and

X-ray images for the SNR size measurements, but there

are still discrepancies greater than 16% and up to 50%.

The discrepancies are caused by the following reasons:

(1) The SNR sizes can be measured only in X-rays and

the surface brightness varies significantly, such as N23,

or the background is complex, such as the Honeycomb

and 0532-67.5; in such cases the discrepancy in size mea-

surements can be as high as 50%. (2) The SNR is su-

perposed on an H II region or a superbubble, whose

Hα emission can confuse the size measurements, such as

N157B and N186D. (3) The SNR size is measured with-

out simultaneously considering optical, X-ray, and ra-

dio images that show wavelength-dependent distribution

of emission, such as 0534−69.9, DEM L238, DEM L299,

and J0550−6823. (4) The irregular shape of an SNR

can cause subjective size measurements to differ by up

to ∼20%, such as N86. For these discrepant objects, we

examine their Hα, [S II], X-ray, and 24 µm images (in

Appendix A), consider radio and kinematic properties

available in the literature, and make new measurements

(described in Appendix B).

The comparisons between Ba2010 and Bo2017 sizes,

right panels of Figure 1, show numerous large discrep-

ancies. These discrepancies are caused by the larger

4

uncertainties in Ba2010 sizes that were compiled from

previous measurements based on mainly X-ray images

and some optical images. As mentioned above and de-

tailed in Appendices A–B, multi-wavelength examina-

tion of an SNR provides the most comprehensive picture

of its physical structure and boundaries, and size mea-

surements based on only one single wavelength may not

reflect the SNR’s true extent.

3. RELATIONSHIP BETWEEN SIZES AND LX

The LMC provides an ideal sample of SNRs for us

to study the relationship between their X-ray luminosi-

ties (LX) and sizes. The size of an SNR may be intu-

itively thought to reflect its evolutionary stage, because

an SNR expands as the shock wave propagates outward

and a large SNR would be older than a small SNR, if

the ambient interstellar densities are similar. However,

the ambient ISM does have a wide variety of physical

properties and conditions, and the relationship between

size and evolution can be quite complex. Through the

relationship between LX and size we hope to investi-

gate effects of ambient environment and evolution on

the SNRs’ X-ray luminosities.

SNRs rarely show round, symmetric shell structures

with well-defined sizes. To assign a “size” to an irregu-

lar SNR, we adopt the average of its major and minor

axes. Such SNR sizes determined from data of Ba2010,

De2010, and Bo2017 are tabulated in Appendix C. As

discussed at length in Section 2, De2010 and Bo2017

sizes were determined primarily with optical and X-ray

images of SNRs and are in agreement for most cases. For

83% of the SNRs that have Bo2017 and De2010 sizes dif-

fer by less than 16%, we adopt their average sizes from

Bo2017. For the SNRs with larger discrepancies between

De2010 and Bo2017, we discuss individual objects and

determine their average sizes in Appendix B, and list

their adopted sizes in the table in Appendix C.

The LMC sample of SNRs have been studied in X-

rays with XMM-Newton by Maggi et al. (2016). They

fit the X-ray spectra with the package XSPEC (Arnaud

1996) using a combination of collisional ionization equi-

librium (CIE) models and non-equilibrium ionization

(NEI) models, derived their X-ray fluxes in the 0.3 to

8 keV band, and computed their LX for an LMC dis-

tance of 50 kpc (Pietrzynski et al. 2013). These observed

(absorbed) LX are listed in the last column of the Table

in Appendix C.

Using the LX and average sizes in Appendix C, we plot

the LX versus size for the LMC SNRs in Figure 2. We

have also made the same LX–size plot with unabsorbed

LX and present it in Figure 3. (These unabsorbed LX

are from the same model fits that produced the absorbed

LX published by Maggi et al. 2016). The distribution

of the SNRs are qualitatively similar to that in Figure

2. Note that we did not include SN 1987A (size= 0.45

pc, LX = 2.7× 1036 ergs s−1) because its inclusion will

leave vast empty space on the left and compress all the

data points on the right in Figure 2 and 3.

At first glance, the LX – size plot for LMC SNRs

shows a scattered diagram; however, if the sizes are di-

vided into three ranges: <10 pc as “small”, 10–30 pc as

“medium”, and >30 pc as “large”, it is possible to see

interesting trends in each size range:

(1) For sizes a few to 10 pc, only a small group of SNRs

exist with LX of a few × 1036 ergs s−1, and all of them

are of Type Ia. For comparison, we add the Galactic

SNRs with sizes a few to 10 pc in Figure 3; the data are

taken from the Chandra Supernova Remnant Catalog2.

Interestingly, Tycho and Kepler SNRs, two small Type

Ia SNRs in our Galaxy, are also located in the similar

part of LX–size plot as the small LMC Type Ia SNRs.

In contrast, the Galactic CC SNR Cas A is an order

of magnitude more luminous than these small Type Ia

SNRs, and the ∼100-year old Galactic Type Ia SNR

G1.9+0.3 is smaller and significantly fainter (Reynolds

et al. 2008; Borkowski et al. 2010, 2013).

(2) For sizes 10–30 pc, there is a bifurcation in the distri-

bution of SNRs. The X-ray-bright ones have LX > 1036

ergs s−1 and the X-ray-faint ones have LX < 1035 ergs

s−1 for sizes below ∼20 pc, and these two groups con-

verge to a few ×1035 ergs s−1 towards 30 pc size. It is

worth noting that the X-ray-faint medium-sized SNRs

are mostly CC SNRs.

(3) For sizes >30 pc, while LX exhibits a wide range,

the majority of the SNRs appear to show a general trend

of LX decreasing with size.

It also appears that the Type Ia SNRs show smaller

scatter in LX for any given size than the CC SNRs,

especially in the medium size range (Figures 2 and 3).

The scatter in LX reflects the ambient interstellar den-

sity: Type Ia SNe occur in diffuse medium with moder-

ate densities, while CC SNe can take place near dense

molecular clouds or in a very low-density environment

produced by energy feedback from massive stars. Be-

cause of the smaller scatter in LX , the smooth variations

of Type Ia SNRs’ LX versus size may demonstrate the

SNR evolution.

The dashed line in the lower right corner of Figure

2 corresponds to a constant surface brightness of 1029

ergs s−1 arcsec−2, which represents the typical detection

limit of the XMM-Newton observations used by Maggi et

2 See http://hea-www.cfa.harvard.edu/ChandraSNR/.

5

Figure 2. Observed LX versus size plot for SNRs in the LMC. The size and LX are listed in Appendix C. For the HoneycombSNR and N86, we have used two extreme size measurements to illustrate the largest uncertainties in the size measurements.Note that some of the large CC SNRs may in fact be Type Ia SNRs whose SN ejecta have cooled and no longer emit detectableX-rays for them to be identified as such.

al. (2016). Consequently, no SNRs are located beneath

this dashed line.

4. DISCUSSION

We have examined the physical structures and envi-

ronments of SNRs in the three size ranges in order to

understand the physical significance of their distribu-

tions in the LX–size plot. The discussion in this section

is ordered according to the SNR sizes.

4.1. Small Known LMC SNRs Are Dominated by Type

Ia

It is striking that the small LMC SNRs, with sizes a

few to 10 pc, are all Type Ia SNRs with LX of a few ×1036 ergs s−1. (Note that SN 1987A is outside the size

range under discussion.) For comparison, we show that

the Galactic Type Ia SNRs Kepler and Tycho are both

located in a similar region as the young LMC Type Ia

SNRs. The small range of LX for small Type Ia SNRs

and the scarcity of small CC SNRs can be explained as

follows.

Type Ia SNe are usually considered to explode in a

tenuous and uniform ISM (e.g., Badenes et al. 2005). On

the other hand, CC SNe usually explode inside interstel-

lar bubbles blown by the fast stellar winds of their mas-

sive progenitors during the main sequence phase (Castor

et al. 1975; Weaver et al. 1977). Interstellar bubble inte-

riors have very low densities, and hence CC SNe inside

bubbles are called “cavity explosions”. It is conceivable

that the interstellar environments of Type Ia and CC

SNe have very different density profiles.

Density profiles of ambient medium strongly affect the

evolution of an SNR’s LX . In a classical model of a

SN explosion in a uniform ISM, the resulting SNR goes

through free expansion phase, Sedov phase (i.e., adia-

batic phase), and radiative phase (Woltjer 1972). The

Sedov phase starts when the swept-up ISM mass is sev-

eral times the SN ejecta mass (e.g., Dwarkadas & Cheva-

lier 1998). The LX of an SNR during the Sedov phase

can be calculated (e.g., Hamilton et al. 1983). To illus-

trate the evolution of LX for different ambient densities,

we plot LX against age and size in Figure 4.

For a Type Ia SNR in a partially neutral ISM, only

the ionized interstellar gas can be swept up by the shock.

Thus, for a uniform density of ∼1 H-atom cm−3 and a

neutral fraction of η, the Sedov phase will start when

the swept-up ionized gas reaches 1.4 M� in mass, cor-

responding to a radius of 2.4(1− η)−1/3 pc. This radius

is 5.2 pc if η = 0.9, and 3 pc if η = 0.5. These sizes

are comparable to the young Balmer-dominated Type

6

Figure 3. Unabsorbed LX versus size plot for SNRs in the LMC.

Figure 4. Evolution of LX in the Sedov model. The ambient density n0 in H-atom cm−3 is marked for each model.

Ia SNRs in the LMC, 0509−67.5 and 0519−69.0; thus,

it is likely that these young Type Ia SNRs are entering

the Sedov phase. However, the interstellar density is so

much lower than the SN ejecta density that their X-ray

emission is still dominated by that produced by the re-

verse shock into the SN ejecta. This is evidenced in the

SN ejecta abundance revealed in the X-ray spectra of

these small Balmer-dominated Type Ia SNRs, although

the X-ray emission shows a shell morphology (Warren

& Hughes 2004; Kosenko et al. 2010). The larger Type

Ia SNRs, such as DEM L71 and 0548−70.4 with sizes in

the 20-30 pc range, must be in the Sedov phase already.

Furthermore, their forward shock and reverse shock have

traveled farther apart, and their X-ray emission shows

7

the forward shock in an interstellar shell well resolved

from the reverse shock in the SN ejecta (Hughes et al.

2003; Hendrick et al. 2003).

X-ray emission from reverse shocks is the cause of the

high LX of small Type Ia SNRs. The small scatter of

these young bright Type Ia SNRs in the LX vs size plot

reflects their similar ages, the relative uniformity of SNe

Ia (in term of nucleosynthesis and explosion energy),

and the modest effect the progenitors have on chang-

ing their immediate surrounding. The smallest Galactic

Type Ia SNR G1.9+0.3 has a low LX because it is so

young (<200 yr) that the reverse shock has only gone

through very little of the SN ejecta (Reynolds et al. 2008;

Borkowski et al. 2014).

For CC SNRs whose SNe exploded in cavities of wind-

blown bubbles, due to the extremely low density within

the bubbles (∼ 10−4 − 10−2 H-atom cm−3), the X-

ray emission from shocked gas would be too faint to

be detected at a young age; only when the SNR’s for-

ward shock hits the dense shell/wall of a bubble will the

X-ray luminosity jump up several orders of magnitude

(Dwarkadas 2005). As shown by Naze et al. (2001), main

sequence O stars have interstellar bubbles of sizes 15–20

pc. By the time a massive star explodes as a CC SN, its

main-sequence bubble has grown larger, and hence the

SNR shock goes through the low-density bubble inte-

rior without producing detectable X-ray emission until

it hits the bubble shell wall at radius of 10 pc or larger.

For illustration, considering a spherical interstellar

bubble with a radius of 10 pc and assuming a simplis-

tic extreme case (upper limit) of average density of 0.01

H-atom cm−3 in the bubble interior, we can calculate

the total mass in the bubble interior to be . 1 M�;

thus, when the SNR shock reaches the bubble wall, it

has swept up only ∼1 M�, much lower than the CCSN

ejecta mass, a few to a few tens M�; thus, the Sedov

phase has not been reached. The bubble shell consists

of swept-up ISM that was originally distributed in the

bubble cavity. Assuming the bubble was blown in a dif-

fuse ISM with density of 1 H-atom cm−3, the total mass

in the bubble shell would be 100 M�; therefore, the SNR

reaches the Sedov phase when the forward SNR shock

traverses the bubble shell.

During the free-expansion phase, the SNR shock is not

significantly decelerated and it remains fast until it hits

the bubble wall. Assuming a constant shock velocity of

10,000 km s−1, it only takes 1000 years for the SNR to

grow to a radius of 10 pc. Consequently, SNRs inside

interstellar bubbles not only emit very faintly in X-rays,

but also expand very rapidly to reach the dense shell

wall. Such “cavity explosions” explain the absence of

small CC SNRs in the LX–size plot. Cavity explosions

are also responsible for the discrepancies between ion-

ization ages and dynamical ages of LMC SNRs, such as

N132D, N63A, and N49B (Hughes et al. 1998).

We have plotted the young CC SNR Cas A in Figure

3 for comparison. Cas A is small in size and luminous in

X-rays. These properties are caused by its interaction

with a dense circumstellar medium, i.e., material ejected

by the SN progenitor (Fesen 2001). Circumstellar bub-

bles are often observed around Wolf-Rayet stars and lu-

minous blue variables (LBVs), and circumstellar bubbles

are smaller than interstellar bubbles (Chu 2003). Cas A

SN must have exploded in a circumstellar bubble.

4.2. X-ray-Bright and X-ray-Faint Medium-Sized

SNRs

The medium-sized LMC SNRs show clear bifurcation

in their LX . In the X-ray-bright group with LX ≥ 1036

ergs s−1, only one is of Type Ia, and the other seven

are CC SNRs. Among these X-ray-bright CC SNRs,

four are interacting with molecular clouds, as CO emis-

sion was detected near the SNRs N23, N49, and N132D

(Banas et al. 1997; Park et al. 2003) and H2 absorp-

tion is detected in Spitzer IRS observations towards

N63A (Segura-Cox et al. 2018, in preparation). None of

these four X-ray-bright CC SNRs show sharp Hα shell

structure enclosing the diffuse X-ray emission, indicat-

ing that the forward SNR shocks are still in the low-

density interiors of bubbles. In the cases of N23 and

N132D, where no prominent shocked cloudlets are seen,

the X-ray emission does show limb-brightening, indicat-

ing that the ambient medium is dense enough to produce

detectable X-ray emission but not optical Hα emission,

and this ambient medium may correspond to the con-

duction layer in a bubble interior (Weaver et al. 1977).

As N23 and N132D are both associated with molecular

clouds, their bubble shells and conduction layers must

have higher densities, which contribute to the bright X-

ray emission. In the cases of N49 (Bilikova et al. 2007;

Park et al. 2012) and N63A (Warren et al. 2003), it

is clear that dense cloudlets, possibly associated with

the molecular clouds, have been shocked and contribute

to the X-ray emission. The other three X-ray-bright

CC SNRs possess bright PWNe: 0540−69.3 (Gotthelf

& Wang 2000), N157B (Wang & Gotthelf 1998), and

0453−68.5 (Gaensler et al. 2003). Pulsars and PWNe

are powerful sources of nonthermal X-ray emission and

provide additional X-ray emission to boost their SNRs’

total LX . Note that the PWN of 0453−68.5 is not par-

ticularly dominating, but its X-ray image show a limb-

brightened sharp shell that indicates that the shock has

already reached the bubble shell. While 0453−68.5 has

8

a PWN, it is the SNR shock impact on the dense bubble

shell giving rise to LX .

The X-ray-faint medium-sized SNRs are mostly asso-

ciated with CC SNe. Among the three X-ray-faint CC

SNRs smaller than 20 pc, 0536−69.2 and [HP99]483 are

not detected in optical, and the Honeycomb SNR shows

only a small patch of honeycomb-like nebulosity result-

ing from SNR shocking a piece of shell wall (Chu et al.

1995; Meaburn et al. 2010). The absence of sharp opti-

cal shells enclosing the diffuse X-ray emission indicates

a low-density ISM around these SNRs. The Honeycomb

SNR has hit a small piece of dense gas and hence it

has the highest LX among these three, but still a cou-

ple orders of magnitude fainter than the SNRs interact-

ing with molecular clouds. The X-ray-faint SNRs with

sizes 20–30 pc all show optical shell structure enclos-

ing their diffuse X-ray emission, and they have higher

LX than the smaller ones, except J0449−6920, whose

XMM-Newton observation was too shallow to make ac-

curate measurements. These CC SNRs may represent

cavity explosions whose SNR shocks have just reached

the bubble shell walls. The SNRs N11L and N120 have

just reached the bubble shell, but the bubble shell den-

sities are not as high as those of N23 and N132D.

4.3. Fading of X-rays in Large SNRs

Among the large (size >30 pc) LMC SNRs, a general

trend of decreasing LX for larger SNRs can be seen, but

for any given size, the differences in LX can be up to

one order of magnitude.

As an SNR sweeps up more interstellar gas, the shock

velocity decreases and when it goes much below ∼300

km s−1, the post-shock temperature will be below 106 K,

too low to generate X-ray-emitting gas. The hot gas in

SNR interior cools, and the X-ray emission diminishes.

The scatter in LX may be caused by the differences

in ambient gas densities (n0) and the SN explosion en-

ergies (E). To evaluate the effects of these two factors,

we consider a spherical SNR of radius R, whose X-ray

emission originates from shocked ISM in a shell. Its LX

is ∝ (emitting volume) × (density)2 × (emissivity). As

(emitting volume) × (density) is proportional to the to-

tal interstellar mass within radius R, it is ∝ R3n20. The

emissivity is a slow function of temperature for photon

energies below 2 keV (Hamilton et al. 1983). Since the

large old SNRs are likely at low X-ray emitting tempera-

tures, a few ×106 K at most, we will treat the emissivity

as a constant, and LX ∝ R3n20.

The total kinetic energy in the SNR shell scales with

the explosion energy, so E ∝ R3n0v2. The large old

SNRs have low expansion velocities of a few ×102 km

s−1, so we will also approximate the expansion velocity

as a constant. Thus, LX ∝ En03. The effects of the

ambient density and the SN explosion energy are about

equally important. However, the ranges of the ambient

gas densities and the SN explosion energies are quite

different. The ambient interstellar density can range

from 0.01 to a few hundred H-atom cm−3, about 4 orders

of magnitude, while the SN explosion energies are mostly

clustered around 1051 ergs with extreme values differing

by no more than 3 orders of magnitude (e.g., Woosley

& Weaver 1986).

Hence, the large scatter in LX for SNRs with the same

size is more likely caused by the detailed differences in

the ambient gas densities, and the SN explosion energy

plays a lesser role in raising the scatter in LX .

5. SUMMARY

The LMC is at a known distance of 50 kpc, and thus

the linear sizes of SNRs in the LMC can be determined

from their angular size measurements (Desai et al. 2010;

Bozzetto et al. 2017), and their X-ray luminosities can

be determined from XMM-Newton X-ray observations

(Maggi et al. 2016), allowing a unique opportunity to

examine the relationship between LX and size of SNRs.

We have critically compared LMC SNR sizes reported

by different authors in the literature and adopted the

most reasonable sizes to investigate how LX vary with

sizes among the LMC sample of SNRs.

We find that the LX – size relationship for LMC SNRs

can be divided into small, medium, and large size ranges:

(1) The small LMC SNRs with sizes a few to 10 pc are

all young Type Ia SNRs with LX a few times 1036 ergs

s−1. The apparent scarcity of small CC SNRs may be

caused by their “cavity explosions”, as massive progen-

itors of CCSNe have blown interstellar bubbles and the

SN explosions take place in the very low-density interi-

ors of the bubbles.

(2) The medium-sized SNRs, with sizes 10–30 pc, show

bifurcation in their LX with an order of magnitude dif-

ference in LX . The X-ray-bright CC SNRs either are

in an environment associated with molecular clouds or

have pulsars and pulsar-wind nebulae emitting nonther-

mal X-ray emission.

(3) The large SNRs, with sizes greater than ∼30 pc,

show a general trend of fading LX at large sizes. As

these sizes are larger than the normal interstellar bub-

bles blown by massive stars, the large SNRs have swept

up the bubble material and extended into the diffuse

3 Note that this is in interesting contrast with the radio lumi-nosity, which scales as Lradio ∝ E1.3n0.45

0 or Lradio ∝ E1.45n0.30

depending on the magnetic field amplification mechanism by theshock (Chomiuk & Wilcots 2009).

9

ISM. As the SNR shocks sweep up more ISM, the shock

velocity slows down. When the post-shock velocities

are too low to produce X-ray-emitting material, the hot

plasma in SNR interiors cool and reduce the X-ray emis-

sion.

This project is supported by Taiwanese Ministry of

Science and Technology grant MOST 104-2112-M-001-

044-MY3.

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10

APPENDIX

A. IMAGES OF THE SNRS WITH LARGE DISCREPANCIES BETWEEN DIFFERENT SIZE

MEASUREMENTS

11

Figure 5. Images of the SNRs with large discrepancies between the size measurements of Bo2017 and De2010.

12

B. DESCRIPTIONS OF SIZE DETERMINATIONS FOR INDIVIDUAL SNRS

N86.– The shape of the SNR is irregular because of the breakout structure in the north, through which the hot gas

flows out from the SNR shell (Williams et al. 1999). For N86 in Figure 2, we have used both sizes of De2010 (75.0

pc, including the breakout) and Bo2017 (61.5 pc, not including the breakout) in the LX – size plot to illustrate the

uncertainty in the size. Only low-resolution ROSAT X-ray images are available for N86; high-resolution Chandra and

XMM-Newton observations will help refine the size determination.

N186D.– The size of SNR N186D in Hα cannot be unambiguously measured, because N186D is projected on the rim

of the superbubble N186E. Through the analysis of velocity fields in N186D, Laval et al. (1989) determined the SNR

size to be ∼40 pc, which is consistent with the size of the [S II]-enhanced shell (see Figure 5 in Appendix A). Based

on these considerations, we adopt the size 36.8 pc given by De2010.

N23.– X-ray emission of N23 is enhanced in the southeast side, likely due to a denser ambient medium (Williams

et al. 1999). The size reported by De2010, 18 × 12 pc, corresponds to only the X-ray-brightest region. Maggi et al.

(2016) and Bo2017 included the fainter X-ray emission from the northwest side and reported a larger SNR size, 23.6

pc, which is more accurate and hence adopted in the LX–size plot in Figure 2.

SNR 0532-67.5.– This SNR may be associated with the OB association LH75 (Chu 1997). This SNR has no optical

counterpart, indicating that it is in a low-density medium, possibly caused by the fast stellar winds and SN explosions

from LH75. The size of this SNR can be measured only in X-rays. There is bright X-ray emission in a ∼ 40 × 20 pc

region, and a fainter and larger X-ray arc connected with the bright region. As in the case of the SNR N23, we include

both the bright and faint X-ray emission regions in the size estimate, and adopt a size of 67.5 pc as the size of SNR

0532-67.5.

SNR 0534-69.9.– The optical images of this SNR show only a faint filament associated with the brightest X-ray

emission region. Chandra observations show the SNR clearly in X-rays, although the southern rim is much fainter

than the rest of the SNR. We have measured and adopted the full extent of the SNR shown in X-rays, about 33.5 pc,

similar as the size measured by Maggi et al. (2016), which is larger than those reported by De2010 and Bo2017.

DEM L238.– Comparing Hα and Chandra images, the X-ray emitting region is larger than the optical shell. We

adopt the full extent of the SNR, 47.5 pc.

Honeycomb.– The Honeycomb SNR is near the 30 Doradus complex, and to the south of the superbubble 30 Dor C.

This region has a very complex star formation history and chaotic nebular morphology. The lack of bright ionized gas

region suggests an evolved environment with low ISM densities. The optical morphology of the SNR is very irregular,

consisting of many cells instead of a simple shell (Chu et al. 1995; Meaburn et al. 2010), leading to large uncertainty

in the determination of SNR size. For the Honeycomb SNR, we have used both sizes of De2010 (15 pc) and Ba2010

(25.5 pc) in the LX – size plot to illustrate the uncertainty in the size.

N157B.– The environment of N157B in Hα is very complex because this SNR is superposed on the HII region of the

OB association LH99 (Chu 1997), and dissected by a foreground dark cloud. The most reliable measurement of the

SNR size is through the analysis of gas kinematics using long-slit high-dispersion spectroscopic observations, 25×18

pc (Chu et al. 1992). This SNR boundary has been confirmed by sharp filaments revealed by HST images as shown

in Figure 5. The size 21.8 pc given by De2010 is taken from Chu et al. (1992).

DEML299.– This SNR is inside a large optical shell. The size reported by De2010 corresponds to the large optical

shell. The X-ray emission actually extends from the shell cavity to the southwest, indicating an outflow. The [S II]/Hα

ratio is enhanced in the shell structure and in the superposed filaments of supergiant shell LMC-2. The SNR is clearly

in a very complex environment. We include all the diffuse X-ray emission region and [S II] enhanced filaments, and

measure a size of 100×50 pc. A smaller SNR size, ∼55 pc, has been reported by Warth et al. (2014) and Maggi et al.

(2016) based on the diffuse X-ray emission and a surrounding [S II]-enhanced filament. The large discrepancy between

these two size measurements illustrate the difficulty in determining SNR sizes in a complex environment confused by

other energetic feedback processes from massive stars. We adopt both 73.5 and 56.5 pc in Table 1 (Appendix C) and

Figure 2.

J0550-6823.– While the diameter of the optical shell is only ∼68 pc, there is X-ray and radio emission extending

over 90 pc in the east-west direction; therefore, we adopt the size of 90×68 pc by Bozzetto et al. (2012).

13

C. SIZES AND X-RAY LUMINOSITIES OF LMC SNRS

Table 1. Sizes and X-ray luminosities of LMC SNRs

SNR J2000 a Other Name Size (Ba2010) Size (De2010) Size (Bo2017) Large Discrepancy b Adopted Size Lxc

(pc) (pc) (pc) (>16%) (pc) (1035ergs/s)

J0448-6700 [HP99] 460 55.0 59.2 60.8 60.8 0.46

J0449-6920 – 33.2 30.0 28.8 28.8 0.07

J0450-7050 SNR 0450-70.9 89.2 97.5 109.4 109.4 0.59

J0453-6655 SNR in N4 63.0 64.5 60.6 60.6 1.17

J0453-6829 SNR 0453-68.5 30.0 30.0 30.4 30.4 13.85

J0454-6713 SNR 0454-67.2 44.2 37.5 32.5 32.5 1.58

J0454-6626 N11L 21.8 18.0 20.4 20.4 0.63

J0455-6839 N86 87.0 75.0 61.5 Y 61.5–75.0 1.42

J0459-7008 N186D 37.5 36.8 29.0 Y 36.8 1.09

J0505-6753 DEM L71 18.0 20.2 18.6 18.6 44.59

J0505-6802 N23 27.8 15.0 23.6 Y 23.6 26.25

J0506-6541 DEM L72 102.0 83.2 96.2 96.2 0.53

J0506-7026 [HP99] 1139 82.5 – 42.5 42.5 1.44

J0508-6902 [HP99] 791 – – 67.0 67.0 0.37

J0508-6830 – – – 30.8 30.8 0.09

J0509-6844 N103B 7.0 7.5 7.0 7.0 51.7

J0509-6731 SNR 0509-67.5 7.25 8.4 7.6 7.6 16.51

J0511-6759 – – – 55.5 55.5 0.16

J0512-6707 [HP99] 483 – – 12.5 12.5 0.09

J0513-6912 DEM L109 53.8 57.8 55.6 55.6 0.51

J0514-6840 – – – 55.0 55.0 0.4

J0517-6759 – – – 66.8 66.8 0.24

J0518-6939 N120 33.5 21.8 23.4 23.4 0.88

J0519-6902 SNR 0519-69.0 7.8 8.2 8.6 8.6 34.94

J0519-6926 SNR 0520-69.4 43.5 33.8 31.2 31.2 2.69

J0521-6543 DEM L142 – 40.5 34.5 34.5 –

J0523-6753 SNR in N44 57.0 52.5 57.5 57.5 0.9

J0524-6624 DEM L175a 58.5 51.8 36.25 36.2 –

J0525-6938 N132D 28.5 26.2 25.5 25.5 315.04

J0525-6559 N49B 42.0 36.0 38.8 38.8 38.03

J0526-6605 N49 21.0 21.0 18.8 18.8 64.37

J0527-6912 SNR 0528-69.2 36.8 35.2 35.0 35.0 1.99

J0527-6550 DEM L204 75.8 67.5 76.2 76.2 –

J0527-6714 SNR 0528-6716 – – 54.0 54.0 0.58

Table 1 continued

14

Table 1 (continued)

SNR J2000 a Other Name Size (Ba2010) Size (De2010) Size (Bo2017) Large Discrepancy b Adopted Size Lxc

(pc) (pc) (pc) (>16%) (pc) (1035ergs/s)

J0527-7104 [HP99] 1234 49.0 – 70.2 70.2 0.25

J0528-6727 DEM L205 – – 55.0 55.0 0.21

J0529-6653 DEM L214 25.0 – 33.1 33.1 1.04

J0530-7008 DEM L218 53.2 47.2 49.4 49.4 0.72

J0531-7100 N206 48.0 45.0 45.0 45.0 2.55

J0532-6732 SNR 0532-67.5 63.0 67.5 45.0 Y 67.5 2.48

J0533-7202 – – – 45.0 45.0 0.57

J0534-6955 SNR 0534-69.9 28.5 23.2 28.8 Y 33.5 6.33

J0534-7033 DEM L238 45.0 40.5 47.5 Y 47.5 1.55

J0535-6916 SN 1987A 0.5 >1.5 0.45 0.45 27.39

J0535-6602 N63A 16.5 19.5 18.5 18.5 185.68

J0535-6918 Honeycomb 25.5 15.0 18.8 Y 15.0–25.5 0.4

J0536-6735 DEM L241 33.8 36.0 34.0 34.0 3.84

J0536-7039 DEM L249 45.0 37.5 39.2 39.2 1.43

J0536-6913 SNR 0536-69.2 120 – 16.5 16.5 0.22

J0537-6628 DEM L256 51.0 48.0 46.9 46.9 0.32

J0537-6910 N157B 25.5 21.8 31.5 Y 21.8 15.0

J0540-6944 SNR in N159 19.5 27.0 26.2 26.2 0.43

J0540-6920 SNR 0540-69.3 15.0 18.0 15.6 15.6 87.35

J0541-6659 [HP99] 456 – – 71.5 71.5 0.77

J0543-6858 DEM L299 79.5 73.5 56.5 Y 56.5–73.5 1.68

J0547-6943 DEM L316B 21.0 46.5 45.0 45.0 1.47

J0547-6941 DEM L316A 14.0 30.0 30.0 30.0 1.26

J0547-7025 SNR 0548-70.4 25.5 28.5 28.1 28.1 2.94

J0550-6823 – 78.0 65.2 81.9 Y 81.9 1.22

aThe 59 confirmed SNRs listed in Maggi et al. (2016).

bSize(De2010)/Size(Bo2017)>1.16 or <0.86.

cTaken from Maggi et al. (2016).